That's one of the questions being debated as Republicans — like all parties that have lost a national election — plot their comeback.

Some think they need to take a new tack on issues such as immigration in order to appeal to changing times and demographic changes. Others believe that the GOP's core conservative principles are still political winners, if delivered in a more convincing manner than was the case during last year's presidential race.

Senators who have been pushing the latter line, such as Ted Cruz of Texas and Rand Paul of Kentucky, are being closely watched at the annual Conservative Political Action Conference meeting this week in the Washington area. Paul got a rousing welcome at his speech Thursday; Cruz is scheduled to give the event's final speech on Saturday.

Some more moderate figures, such as New Jersey Gov. Chris Christie, are notable by their absence.

But a party's course is not charted solely by the figures who draw the most attention from media. Officials at all levels of government, as well as activists, will be debating the best way to go over the coming months and years.

What course they favor depends not only on their beliefs, but also on the roles they play within the political ecosystem. So it's worth looking at a few figures who in their various ways demonstrate the GOP's different possibilities (and tensions).

The Purist: Thomas Massie

For all the attention the so-called Tea Party Class of 2010 got for being conservative and unyielding, the smaller number of Republicans elected to the House last fall may arguably be more loath to compromise.

"In this class, there's a higher concentration of fiscal conservatives," says Barney Keller, a spokesman for the conservative Club for Growth.

Among their number, Keller counts Rep. Thomas Massie, who was first elected in November from a district in northern Kentucky. A county official and MIT-trained scientist and entrepreneur, Massie upset two better-established candidates to win the GOP primary — with backing not only from the Club for Growth, but also a superPAC established by a wealthy college student.

"Massie doesn't owe his political heritage to any person on the moderate side, or however you would describe the mainstream Republican Party in this area," says John T. Spence, a political scientist at Thomas More College in Crestview Hills, Ky. "He just doesn't."

In his short time in Washington, Massie has continued to demonstrate that he won't be beholden to party leaders, voting against the budget deal in January that averted the fiscal cliff and let an automatic tax increase kick in for the wealthy, and also voting against John Boehner for House speaker. (Massie favored fellow firebrand Justin Amash of Michigan.)

"If he believes in something, he's not going to back down, even though within his own party he might go against their agenda," says Mike Karem, a Louisville-based strategist and official in several GOP administrations.

The few bills Massie has co-sponsored thus far demonstrate clear conservative leanings, including proposals to abolish the Affordable Care Act, the Federal Reserve and gun-free school zones.

All of that is in keeping with the preferences of most people in his district, Spence says.

"With guys like Thomas Massie, you're going to see somebody who stands on principle, not just at election time, but every time," says Keller, of the Club for Growth.

The Pragmatist: Bill Haslam

Bill Haslam, the governor of Tennessee, has lately been getting the kind of attention that in the past politicians might have basked in, but which now makes them a little nervous.

His record on issues such as education and economic development have won him praise at home and from Washington outlets such as Politico, which called him "The GOP star you've never heard of."

During the governors' meeting last month in Washington, Haslam was singled out for praise by President Obama, who noted that the governor understood the value of compromise in getting things done.

Of course, Republicans don't generally welcome the embrace of this particular president. Kind words for Obama in the aftermath of Superstorm Sandy are arguably the main reason Gov. Christie has become persona non grata at gatherings like CPAC.

"Few if any Republicans in the state would want an endorsement from President Obama," says Mark Byrnes, a political scientist at Middle Tennessee State University. And Haslam has had to disavow having his head turned by praise from the national press.

But the real fine line that Haslam has to walk, Byrnes says, is not between attention and humility but between the Republican-dominated Legislature and his constituents.

Since taking power a couple of years ago, legislators have debated controversial bills in areas such as gun rights, school prayer and evolution. Haslam has sometimes signed off on their legislation, but has made clear they're not his top priorities.

"A lot of folks who would support him would support those social measures, so he doesn't want to totally reject them," Byrnes says. "But on the other hand, he's made it clear they're not his top priorities."

Bread-and-butter fiscal issues are. Haslam has managed to cut taxes, changed tort and workers' compensation laws, and pursued a string of education measures, including one to make it harder for K-12 teachers to win tenure.

His accomplishments have helped Tennessee score high when states are ranked by such measures as relative tax burden and their business environments.

A recent MTSU poll showed that far more Republicans in the state believe their party should become more conservative than more moderate, but Haslam's personal approval ratings are among the highest in the country.

"There is wide agreement among Memphis business leaders — Republican and Democrat alike — that Haslam's pragmatism and good business sense are paying dividends for Tennessee," says Blair Taylor, president of Memphis Tomorrow, a business group.

The Activist: Melissa Clouthier

Melissa Clouthier never intended to devote all her time to conservative messaging. It just worked out that way.

Clouthier is a chiropractor outside Houston who started a blog after her first child was born. Within a few days, she says, she found herself writing about politics because issues such as health care and carving out a promising future for children are inevitably political in nature.

"Yes, I'm pushing a conservative-libertarian point of view because I think it's better for people," she says. "It's more loving and more caring."

Her writings — sometimes wry, sometimes caustic, occasionally profane — quickly drew the attention of prominent conservative voices such as Glenn Reynolds. She found herself getting asked for help with public relations by the late conservative media mogul and provocateur Andrew Breitbart.

About 15 months ago, she stopped seeing patients and devoted herself full-time to hosting podcasts and leading social-media training seminars. She blogs for various outlets and sends out tweets. Lots of tweets, sometimes dozens a day.

"She's not a household name, but she's a thought leader in the right-of-center blogosphere, no question about it," says David Carney, a GOP consultant and longtime strategist for Texas Gov. Rick Perry. "She's one of the outside-the-Beltway drivers of conservative thought."

Moving to Texas after living in high-tax states such as Michigan, New York and California convinced her that lower taxes and less government regulation offers a better future to people than government-assistance programs such as Medicaid and Obamacare.

"If you look at concrete outcomes, it's better in places that are putting in place a more conservative worldview," Clouthier says.

She sees her role as not only promoting that worldview, but also holding accountable through continual criticism both media outlets and politicians who would promote "big government," including Republicans.

"That's what pragmatism gets us," she says. "This is why, when it comes to policy positions, I don't want the Republicans to be the Chris Christies of the world. While the media loves them in the short term, the long-term outcomes are not good."

The Party Leader: Jim Brulte

Arguments about the future of the national Republican Party have been anticipated over the past decade in California.

"California did arrive at this deep dark hole sooner than the national party because the demographic changes happened faster than they did in the rest of the country," says Bruce Cain, a political scientist at Stanford University.

Of course, Republicans are in much worse shape in California than they are nationally. The GOP's share of registered voters in California is below 30 percent, and Democrats there won two-thirds majorities in both legislative chambers last fall.

Taking on the task of rebuilding the party's fortunes is Jim Brulte, a former top GOP leader in both the California Assembly and the state Senate. He became the California Republican Party chairman earlier this month.

"His challenge is tremendous," says Dan Schnur, a former Republican strategist who is now at the University of Southern California. "It's become a cliche, but the party has really bottomed out."

Brulte has avoided making sweeping statements about the direction in which he hopes to lead the party. "He's concentrating on blocking and tackling right now," says his spokesman, Mark Standriff — raising money and talking to political leaders.

Beyond improving party operations, though, it's not entirely clear from Brulte's record how he intends to proceed. He has talked for years about the need for the GOP to do a better job reaching out to women and minorities. He's a conservative, but he cares about winning elections in an increasingly blue state.

But Brulte himself has been a polarizing force. As a legislative leader, he punished Republicans who strayed from the party line and voted with Democrats on budgets.

"He perfected the technique of intimidating people in the primary into towing the party line," Cain says.

Even if Brulte were inclined to take the California GOP in a more moderate direction, it's not certain he'd meet with success. Former GOP Gov. Arnold Schwarzenegger sought just such a path and ended up a much-reviled figure among more conservative rank-and-file Republicans.

Business groups have promoted any number of structural changes through ballot initiatives in recent years, such as handing redistricting to a commission and changing the primary selection system. Those moves were motivated at least in part, Cain says, by the desire to make the Republican Party more moderate.

Still, a succession of electoral losses may convince GOP activists to open up their ears to new calls for a different approach, Schnur says. If anyone can convince them, Brulte may be the man.

"Jim is the perfect example of a very principled conservative who understands that the party can't succeed without principled conservatives," Schnur says, "but it can't succeed without expanding its reach, as well."